MathPlotAI Logo MathPlotAI

Triangle Area - Height Outside Rectangle

Triangle Area - Height Outside Rectangle
Loading the math board and drawing, please wait…
2019-04-05 11:37
TrianglePolygonTransformationGeometric Construction
This example demonstrates how to calculate the area of a triangle with its height located outside a rectangle. Key math concepts include triangle area formula, rectangle properties, rotation transformation, and midpoint theorem. Constructed using commands like Segment, Point, Midpoint, Rotate, Polygon, RotateText, Intersect, Translate. Suitable for high school mathematics teaching, emphasizing the integration of area calculation and geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(M, D) → g
  2. Point(g) → E
  3. Midpoint(A, E) → I
  4. Rotate(I, k1, I) → I'
  5. Midpoint(E, B) → J
  6. Rotate(J, (-k1), J) → J'
  7. Polygon(A, B, J', G) → q1, f, h, i, k
  8. Polygon(A, B, E) → t1, e, a, b
  9. Rotate(E, k1, I) → E'
  10. Rotate(E, (-k1), J) → E'_1
  11. Segment(B, E) → m
  12. Segment(E, A) → n
  13. Segment(A, B) → p
  14. Segment(B, H) → q
  15. Segment(H, G) → r
  16. Segment(G, A) → s
  17. Segment(A, B) → t
  18. Segment(B, C) → c
  19. Segment(C, D) → d
  20. Segment(D, A) → f_1
  21. RotateText(text1, π / 2) → text3
  22. Rotate(E, (-k1), J') → E'_2
  23. Polygon(I, J, E) → t2, e_1, i_1, j
  24. Intersect(e_1, j) → F
  25. Point(e) → L
  26. Polygon(F, K, L) → t3, l, f_2, k_1
  27. Rotate(I, (-k1), J') → I'_1
  28. Rotate(J, (-k1), J') → J'_1
  29. Rotate(E, (-k1), J') → E'_3
  30. Polygon(I'_1, J'_1, E'_3) → t2', e'_3, i'_1, j'_1
  31. Translate(F, Vector[A, (x(A) + ((x(B) - x(A)) * k1 / π), y(A))]) → F'
  32. Translate(K, Vector[A, (x(A) + ((x(B) - x(A)) * k1 / π), y(A))]) → K'
  33. Translate(L, Vector[A, (x(A) + ((x(B) - x(A)) * k1 / π), y(A))]) → L'
  34. Polygon(F', K', L') → t3', l', f', k'